Courses News

Monday, January 23, 2017 - 11:21

Les notes manuscrites du troisième cours d'Alain Comtet sur le
mouvement brownien sont maintenant disponibles. Voir la page web du cours:

Tuesday, January 17, 2017 - 13:30

Les notes manuscrites du deuxième cours d'Alain Comtet sur le mouvement brownien sont maintenant disponibles. Elles peuvent se lire indépendamment du premier cours. Voir la page web du cours:

On cherche toujours des volontaires pour traduire ces notes en Latex, et éventuellement en Anglais, et éventuellement les améliorer en collaboration avec l'orateur.

Tuesday, January 3, 2017 - 09:53

La seconde série de cours de l'IPhT de l'année académique commence ce vendredi 6 janvier 2017 à 10h, avec un cours en français d'Alain Comtet sur les fonctionnelles browniennes et leurs applications.

Le mouvement brownien est d'abord un phénomène naturel, décrit par le botaniste Robert Brown en 1828, puis étudié par des sommités de la physique et des mathématiques, dont Albert Einstein, Marian Smoluchowski, Paul Langevin, Jean Perrin, Norbert Wiener, Andrey Kolmogorov et Paul Lévy.

Son idéalisation par Paul Lévy a conduit à l'un des objets mathématiques les plus étudiés en théorie des probabilités. Une grande variété de problèmes de physique statistique peuvent se reformuler en termes de fonctionnelles plus ou moins complexes du mouvement brownien unidimensionnel.

Alain Comtet, chercheur au LPTMS à Orsay et professeur émérite à l’Université Pierre et Marie Curie, est un physicien renommé pour ses travaux sur les systèmes de basse dimension, les systèmes désordonnés classiques et quantiques, et les processus stochastiques en général.

Pour un résumé détaillé et les horaires complets, voir la page web du cours:

Friday, June 10, 2016 - 15:50

Dear all,

handwritten, draft notes for lecture #2 of Caprini's course 'Gravitational waves' are available online.

The organizers

Friday, June 3, 2016 - 16:07

Dear all,

handwritten, draft notes for lecture #1 of Caprini's course 'Gravitational waves' are online.

The organizers

Wednesday, May 25, 2016 - 12:08

The fifth and last IPhT course of this academic year will start on Friday, June 3rd, with the first of a series of five lectures by Chiara Caprini on Gravitational waves. For the abstract and further details, see the course's web page.

The lectures are open to all: students, postdocs and researchers, whether IPhT members or outsiders. Do not hesitate to recommend them to anyone who might be interested.

We are looking for volunteers who would type lecture notes under the supervision of the speaker. Please contact the organizers (or the speaker) if you are interested.

Thursday, May 19, 2016 - 10:55

Summary of second Volin's lecture 'Quantum integrability: old and new tools' (tomorrow Friday May 20th at 10:00). Knowledge of the material from the previous lecture is desirable but not compulsory.

Part IA: Notion of a quantum spectral curve (QSC) is introduced and it is explained in what sense it is a quantisation of a classical curve. Discussion includes the historically first example: relation between Schrodinger and Hamilton-Jacobi equations. On the next step, we introduce a geometric description of QSC for systems with GL(N) symmetry as a special-type section of a holomorphic bundle with fiber being the maximal flag of C^N. This construction naturally arises whenever we solve order-N differential or finite-difference equations. Symmetries behind the geometric constructions are discussed.

Part IB: We discuss the ring of supersymmetric polynomials and demonstrate its isomorphism to the ring of symmetric polynomials, in the case N=infty, M=infty (superduality). Inspired by these observation, we translate these ideas to relation between GL(N|M) and GL(N+M) QSC's thus effectively formulating QSC for GL(N|M) case. Part I is finalised by a practical example: new efficient way to solve Bethe equations for rational spin chains (including the Heisenberg XXX).

Part IIA (After coffee break): Baxter equation has two solutions. We discuss the role of the dominant and subdominant solutions for the case of compact SU(2) and non-compact SL(2) spin chains. Non-compact case is rich with Stoke's phenomena; it also brings us the need to perform Borel re-summation, prescription for the latter naturally introduces the notion of QSC analytic in the upper or lower half-planes.

Part IIB: We motivate and formulate QSC that encodes the spectrum of planar N=4 SYM.

Thursday, May 12, 2016 - 16:04

Dear all, please find below a short summary of the first Volin's lecture, to be held tomorrow at 10:00 in IPhT.

The Organizers

Part 1 (before coffee break):

Bethe equations for the spectrum of anharmonic oscillator.

We will depart from the Schrodinger equation with polynomial potential,
discuss WKB approximation, Stokes phenomena, and derive the Bohr-Sommerfeld
quantization condition using very basic analytic continuation arguments.
Then we discuss the full quantum picture and show that the spectral
determinants for this system obey certain Wronskian relations which lead to
Bethe equations on the Hamiltonian's eigenvalues.

Part 2 (after coffee break)

Characters and integrability

We will recall some basic facts about Schur-Weyl duality and character
formulae. Then the discussion of SU(N) XXX spin chain from this perspective
is due, with the goal to introduce the concept of transfer matrices and
Hirota equations. We end up with presenting Wronskian solution of the
Hirota equations and Wronskian relations on Baxter Q-functions which, for
the SU(2) case, happen to be identical to those we observed when solving
the anharmonic oscillator.

Time permitting, generalization to non-compact supersymmetric cases will be
given, otherwise it is the first topic of the lecture next week.

Monday, May 9, 2016 - 17:13

Dear all,

The second part of the course 'Quantum integrability: old and new tools', held by Dmytro Volin, will start on next Friday, 13th May at 10:00AM.

Dmytro proposes to give 1-2 supplementary exercise sessions: we will discuss this possibility Friday.

The organizers

PS Draft notes for Serban's lectures are available here:

Thursday, April 14, 2016 - 15:20

Dear all,

(draft) notes including the second lecture of the course "Integrability: old and new tools", written by D. Serban, are available online:
See you tomorrow for the third lecture.
The organizers


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